Lefroy said a fourth diamond core hole is now underway to an estimated final depth of 560m, with assays from earlier holes due late next month.
Burns is part of Lefroy's namesake gold project 50km south east of Kalgoorlie.
The copper and gold mineralisation hosted by both porphyry and basalt is considered by Lefroy to be a new style of mineralisation in the area, a land position "dominated" by Lefroy.
A 14-hole diamond program started in April.
Lefroy started the current quarter with A$2.9 million cash, suggesting a capital raising in the short term.
Shares in Lefroy were up 8% to $1.08 in morning trade, capitalising the company at $129 million.
The stock was at levels around 20c earlier this year prior to the big Burns drill hit.